Problem: Rewrite as a simplified fraction. ${0.30\overline{4} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 304.4444...\\ 100x &= 30.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 274}$ ${x = \dfrac{274}{900}} $ ${x = \dfrac{137}{450}} $